Question: The sum of two numbers is $58$, and their difference is $12$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 58}$ ${x-y = 12}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 70 $ $ x = \dfrac{70}{2} $ ${x = 35}$ Now that you know ${x = 35}$ , plug it back into $ {x+y = 58}$ to find $y$ ${(35)}{ + y = 58}$ ${y = 23}$ You can also plug ${x = 35}$ into $ {x-y = 12}$ and get the same answer for $y$ ${(35)}{ - y = 12}$ ${y = 23}$ Therefore, the larger number is $35$, and the smaller number is $23$.